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This paper explores fast, polynomial time heuristic approximate solutions tothe NP-hard problem of scheduling jobs on N identical machines. The jobs areindependent and are allowed to be stopped and restarted on another machine at alater time. They have well-defined deadlines, and relative prioritiesquantified by non-negative real weights. The objective is to find scheduleswhich minimize the total weighted tardiness (TWT) of all jobs. We show how thisproblem can be mapped into quadratic form and present a polynomial timeheuristic solution based on the Hopfield Neural Network (HNN) approach. It isdemonstrated, through the results of extensive numerical simulations, that thissolution outperforms other popular heuristic methods. The proposed heuristic isboth theoretically and empirically shown to be scalable to large problem sizes(over 100 jobs to be scheduled), which makes it applicable to grid computingscheduling, arising in fields such as computational biology, chemistry andfinance.

A novel Hopfield neural network approach for minimizing total weighted tardiness of jobs scheduled on identical machines